Optimized aerodynamic profile for a turbine vane, in particular for a nozzle of the fourth stage of a turbine

ABSTRACT

When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y, Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point under consideration from a first reference plane P 0  situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P 1 . The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This patent application claims the benefit under 35 U.S.C. §119 to U.S.Provisional Application No. 62/361,540, filed on Jul. 13, 2016, theentirety of which is incorporated herein by reference.

FIELD OF THE DISCLOSURE

The present invention relates to an aerodynamic profile for a turbinevane.

INTRODUCTION

In particular, the invention relates to the aerodynamic profile of anozzle vane forming a portion of the stator of a gas turbine, and moreparticularly of a low pressure turbine of the type used in a turbojet ofan aircraft.

The invention relates in particular to a nozzle vane of the fourth stageof a turbine having a plurality of stages, preferably seven stages.

Such a profile should enable the turbine to provide the desiredefficiency, and in order to do that it must be such that the flow of airaround the profile is sound over the working spectrum of the turbine,i.e. substantially such that it does not give rise to turbulence, whichis harmful for overall efficiency.

It must be capable of being installed properly in the environment of theengine, and in particular, for a nozzle vane forming a portion of thestator of the turbine, it must be capable of being fastened easily tothe sectors of the foot platform (the zone of the vane that is furthestfrom the axis of rotation of the turbine) and of the head platform (thezone that is closest to said axis). Furthermore, this part must presenta profile enabling it to be manufactured in a reliable andcost-effective manner by available manufacturing methods, such ascasting, forging, machining, additive fabrication, or else weaving,without this list being limitative.

Furthermore, the profile of the vane must enable it to withstand themechanical stresses, to which the vane is subjected, by enabling thosestresses to be spread over the entire vane in such a manner as to avoidpremature wear thereof. This spreading must apply both in static modeand in dynamic mode.

An object of the invention is to propose an aerodynamic profile for aturbine vane that is optimized, and capable of satisfying thoseobjectives.

This object is achieved by the fact that when cold and in a non-coatedstate, said profile is substantially identical to a nominal profiledetermined by the Cartesian coordinates X,Y,Zadim given in Table 1, inwhich the coordinate Zadim is the quotient D/H where D is the distanceof the point P under consideration from a reference X,Y plane situatedat the base of the nominal profile, and H is the height of said profilemeasured from said reference plane that is the intersection of thestacking axis of the set of vanes and the axisymmetric surface of thehub, out to a second reference plane that is the intersection of saidstacking axis with the axisymmetric surface of the casing, themeasurements D and H being taken radially relative to the axis of theturbine, while the coordinate X is measured in the axial direction ofthe turbine.

This profile has been determined as a result of numerous tests andsimulations. It is defined cold, i.e. at an ambient temperature of 20°C. That is a reference temperature at which the profile is geometricallydetermined. The above-mentioned objectives of aerodynamics andmechanical optimization are naturally valid for the conditions of use ofthis aerodynamic profile, i.e. when hot, at a temperature that isstabilized when the engine of which the turbine forms a part is beingused under cruising conditions.

Furthermore, the aerodynamic profile of the invention is defined in thenon-coated state. Since turbine vanes are subjected to high temperaturegradients, it is common practice for them to be provided with a coatinghaving thermal properties enabling them more easily to withstand suchtemperature variations. The profile is determined prior to installingsuch a coating.

It is stated above that the profile of the invention is “substantiallyidentical” to the nominal profile. This means that the profile maydepart very slightly from said nominal profile.

The aerodynamic profile is thus preferably defined within an envelope of±1 millimeter (mm) in a direction normal to the surface of the nominalprofile.

This variation takes account in particular of manufacturing tolerancesof the profile.

It is also preferable for the X,Y coordinates of the aerodynamic profileto lie within a range of ±5% relative to the X,Y coordinates of thenominal profile.

This variation takes account of the setting of the profile to adapt tothe flow coming from the blades of the turbine situated upstream, so asto further improve the efficiency of the turbine. In particular, theprofile is adapted so as to be optimized for the flow coming from therotary wheel of the third stage of a turbine when the vane of theinvention belongs to the nozzle of the fourth stage of a turbine.

With a nozzle vane, i.e. a portion of the stator of a turbine, theprofile serves to orient the fluid correctly for the turbine blades thatare situated downstream, and that belong in particular to the rotarywheel of the fourth stage of the turbine.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention can be better understood and its advantages appear betteron reading the following detailed description of an embodiment given byway of non-limiting example. The description refers to the accompanyingdrawings, in which:

FIG. 1 is a fragmentary axial section view of a turbine including a vaneof profile that corresponds to that of the invention;

FIG. 2 is an enlarged view of FIG. 1, showing the fourth stage of theturbine.

DETAILED DESCRIPTION

The turbine shown in axial section in FIG. 1 comprises seven stagesreferenced respectively S1 to S7. In the direction DF going fromupstream to downstream, each stage comprises a nozzle that forms aportion of the stator of the turbine and that has a plurality ofradially-oriented vanes, and a rotary wheel that forms a portion of therotor of the turbine and that likewise includes a plurality ofradially-oriented blades.

In FIG. 1, the vanes of the nozzles of stages S1 to S7 are givenreferences N1 to N7, whereas the blades of rotary wheels of stages S1 toS7 are given respective references W1 to W7.

In known manner, the vanes of the nozzles are fastened at both ends tostationary structure portions, while the blades of the rotary wheels arefastened to a rotary disk via their roots that are formed at theirradially-inner ends closer to the axis of the rotation A of the turbine.The disks d1 to d7 forming parts of the wheels W1 to W7 are constrainedto rotate together.

The invention relates in particular to a vane N4 which is a vane of thenozzle of the fourth stage S4 of the turbine that, as mentioned above,preferably comprises seven stages as shown, without this number beinglimiting.

As best seen in FIG. 2, via its foot 10, which is its end remote fromthe axis of rotation A, the vane N4 is fastened to the outer ring 12 ofthe turbine, which ring is stationary in rotation. Via its head 14,formed by its end closer to the axis of rotation A, the vane is fastenedto an inner shroud 16 of the turbine. By convention, the aerodynamicprofile 18 of the vane is the entire portion of said vane that extendsradially outwards from its head 14 to its foot 10 without incorporatingthe fastenings respectively to the outer ring 12 and to the inner shroud16.

In FIG. 2, there can be seen a frame of reference comprising Cartesiancoordinates X,Y,Z. The radial direction Z is the height direction of thevane, which extends radially from its head to its foot. This direction Zis perpendicular to the axial direction X which is the direction of theaxis of rotation A of the turbine. The direction Y is perpendicular tothe X,Z plane and is therefore tangential to the direction of rotationof the turbine.

The nominal profile from which the aerodynamic profile of the inventionis determined is defined in following Table 1 of coordinates, in whichthe coordinate Zadim, measured along the axis Z is non-dimensional,whereas the dimensions X and Y, respectively measured along the axes Xand Y, are expressed in millimeters.

TABLE 1 X Y Zadim −18.2402 3.758554 −0.12475 −18.27 3.720186 −0.12475−18.3072 3.660284 −0.12475 −18.3501 3.560279 −0.12475 −18.377 3.411151−0.12475 −18.3647 3.213759 −0.12475 −18.2992 2.975383 −0.12475 −18.17522.703836 −0.12475 −17.9914 2.404749 −0.12475 −17.7462 2.083467 −0.12475−17.4376 1.746352 −0.12475 −17.0631 1.401188 −0.12475 −16.6204 1.057975−0.12475 −16.1072 0.729966 −0.12475 −15.5228 0.432395 −0.12475 −14.86790.185889 −0.12475 −14.148 0.013132 −0.12475 −13.3743 −0.06045 −0.12475−12.565 −0.01729 −0.12475 −11.7423 0.150901 −0.12475 −10.9271 0.43848−0.12475 −10.1318 0.825676 −0.12475 −9.36127 1.290573 −0.12475 −8.617451.815148 −0.12475 −7.90294 2.387476 −0.12475 −7.21954 2.996957 −0.12475−6.56786 3.63334 −0.12475 −5.95149 4.29054 −0.12475 −5.37343 4.962303−0.12475 −4.83887 5.644481 −0.12475 −4.34726 6.328699 −0.12475 −3.892577.00374 −0.12475 −3.48118 7.667755 −0.12475 −3.10698 8.311363 −0.12475−2.7677 8.928541 −0.12475 −2.45901 9.512949 −0.12475 −2.17861 10.06008−0.12475 −1.92437 10.5662 −0.12475 −1.69476 11.02847 −0.12475 −1.4880111.44463 −0.12475 −1.30377 11.81372 −0.12475 −1.14135 12.13535 −0.12475−1.00081 12.4102 −0.12475 −0.88186 12.6396 −0.12475 −0.78408 12.82565−0.12475 −0.70777 12.97181 −0.12475 −0.70582 13.09209 −0.12475 −0.7527213.16344 −0.12475 −0.79445 13.19789 −0.12475 −0.83134 13.21704 −0.12475−0.86384 13.22779 −0.12475 −0.90787 13.23491 −0.12475 −0.97833 13.23046−0.12475 −1.06692 13.18651 −0.12475 −1.13936 13.07185 −0.12475 −1.2313412.92537 −0.12475 −1.34642 12.74654 −0.12475 −1.48647 12.53458 −0.12475−1.6528 12.2891 −0.12475 −1.84634 12.01019 −0.12475 −2.06852 11.69894−0.12475 −2.31666 11.35417 −0.12475 −2.59955 10.9839 −0.12475 −2.9245610.59735 −0.12475 −3.29423 10.2008 −0.12475 −3.70913 9.79744 −0.12475−4.16883 9.389512 −0.12475 −4.67019 8.979379 −0.12475 −5.20776 8.569188−0.12475 −5.77418 8.159969 −0.12475 −6.36031 7.751641 −0.12475 −6.956147.343748 −0.12475 −7.55179 6.930359 −0.12475 −8.14257 6.514699 −0.12475−8.72824 6.102633 −0.12475 −9.31469 5.698159 −0.12475 −9.91144 5.305774−0.12475 −10.5305 4.929263 −0.12475 −11.1751 4.577391 −0.12475 −11.83354.266935 −0.12475 −12.4833 4.01358 −0.12475 −13.1011 3.824332 −0.12475−13.6734 3.695956 −0.12475 −14.1966 3.619384 −0.12475 −14.6773 3.584558−0.12475 −15.1269 3.583842 −0.12475 −15.5559 3.613105 −0.12475 −15.9653.66965 −0.12475 −16.3466 3.748794 −0.12475 −16.6958 3.842304 −0.12475−17.0147 3.936167 −0.12475 −17.3093 4.010132 −0.12475 −17.5805 4.037479−0.12475 −17.8134 4.014628 −0.12475 −17.9895 3.956055 −0.12475 −18.1043.888866 −0.12475 −18.1736 3.83045 −0.12475 −18.4065 3.915947 −0.07143−18.4392 3.877184 −0.07143 −18.4799 3.815783 −0.07143 −18.5257 3.711889−0.07143 −18.5541 3.556226 −0.07143 −18.5416 3.350068 −0.07143 −18.47513.100618 −0.07143 −18.3493 2.815408 −0.07143 −18.1627 2.499917 −0.07143−17.9135 2.159357 −0.07143 −17.5995 1.799936 −0.07143 −17.2182 1.429319−0.07143 −16.7668 1.057343 −0.07143 −16.2427 0.696933 −0.07143 −15.64430.364019 −0.07143 −14.972 0.077857 −0.07143 −14.2294 −0.13725 −0.07143−13.4264 −0.25655 −0.07143 −12.5802 −0.25524 −0.07143 −11.7135 −0.12229−0.07143 −10.8511 0.143853 −0.07143 −10.0117 0.528811 −0.07143 −9.206131.012327 −0.07143 −8.43983 1.574349 −0.07143 −7.71573 2.198316 −0.07143−7.03441 2.869095 −0.07143 −6.39456 3.572759 −0.07143 −5.79658 4.299083−0.07143 −5.24149 5.039498 −0.07143 −4.73096 5.786709 −0.07143 −4.262416.531291 −0.07143 −3.83043 7.263171 −0.07143 −3.4381 7.978256 −0.07143−3.08029 8.668392 −0.07143 −2.75426 9.327577 −0.07143 −2.45684 9.950315−0.07143 −2.1858 10.53226 −0.07143 −1.93933 11.06985 −0.07143 −1.7163711.56053 −0.07143 −1.51558 12.00224 −0.07143 −1.33673 12.39411 −0.07143−1.17926 12.73579 −0.07143 −1.04321 13.02801 −0.07143 −0.92825 13.27212−0.07143 −0.83389 13.47025 −0.07143 −0.76022 13.62579 −0.07143 −0.7519813.75189 −0.07143 −0.79659 13.82907 −0.07143 −0.83916 13.86617 −0.07143−0.87754 13.88641 −0.07143 −0.91161 13.89721 −0.07143 −0.95782 13.90294−0.07143 −1.03059 13.8925 −0.07143 −1.11883 13.83725 −0.07143 −1.1911113.71552 −0.07143 −1.2824 13.55966 −0.07143 −1.39569 13.36867 −0.07143−1.53243 13.14134 −0.07143 −1.69368 12.87701 −0.07143 −1.87989 12.57534−0.07143 −2.09195 12.23697 −0.07143 −2.32933 11.86226 −0.07143 −2.5971311.45592 −0.07143 −2.90281 11.02572 −0.07143 −3.25169 10.57951 −0.07143−3.64697 10.12413 −0.07143 −4.08679 9.662374 −0.07143 −4.56882 9.197095−0.07143 −5.08914 8.730195 −0.07143 −5.64217 8.262362 −0.07143 −6.220717.792875 −0.07143 −6.81618 7.320933 −0.07143 −7.4202 6.837768 −0.07143−8.02595 6.346509 −0.07143 −8.63056 5.85568 −0.07143 −9.24383 5.376959−0.07143 −9.87074 4.92121 −0.07143 −10.5139 4.499083 −0.07143 −11.17024.123375 −0.07143 −11.8285 3.806461 −0.07143 −12.4735 3.555708 −0.07143−13.0914 3.371675 −0.07143 −13.6747 3.24832 −0.07143 −14.2234 3.177176−0.07143 −14.7418 3.150413 −0.07143 −15.2372 3.162254 −0.07143 −15.71213.208785 −0.07143 −16.1619 3.286356 −0.07143 −16.5765 3.389318 −0.07143−16.9471 3.511657 −0.07143 −17.2681 3.646215 −0.07143 −17.539 3.781393−0.07143 −17.7649 3.906907 −0.07143 −17.9562 4.004266 −0.07143 −18.12164.046287 −0.07143 −18.25 4.030715 −0.07143 −18.3316 3.985547 −0.07143−18.6094 4.107134 0 −18.6457 4.067881 0 −18.6906 4.004555 0 −18.74023.895658 0 −18.7701 3.73163 0 −18.7573 3.514308 0 −18.6892 3.250856 0−18.5606 2.94849 0 −18.3698 2.612515 0 −18.115 2.248005 0 −17.79361.861012 0 −17.403 1.459092 0 −16.9401 1.05194 0 −16.4018 0.652303 0−15.7859 0.275787 0 −15.0916 −0.05733 0 −14.3214 −0.32323 0 −13.4832−0.49497 0 −12.5928 −0.54565 0 −11.6731 −0.45451 0 −10.7531 −0.21316 0−9.85891 0.170835 0 −9.00922 0.678985 0 −8.21442 1.288278 0 −7.478451.976096 0 −6.80046 2.721545 0 −6.17674 3.506233 0 −5.60334 4.315196 0−5.07849 5.13727 0 −4.59904 5.961832 0 −4.15984 6.77843 0 −3.756457.578188 0 −3.38768 8.354746 0 −3.04992 9.101219 0 −2.7399 9.811614 0−2.45597 10.48128 0 −2.19609 11.10598 0 −1.95881 11.68237 0 −1.7436912.20811 0 −1.54991 12.68137 0 −1.37743 13.10132 0 −1.22584 13.46774 0−1.09513 13.78132 0 −0.98493 14.04348 0 −0.89468 14.25645 0 −0.8241914.42352 0 −0.80834 14.55657 0 −0.8501 14.64067 0 −0.89374 14.68106 0−0.93402 14.70267 0 −0.97102 14.71383 0 −1.0212 14.71793 0 −1.0984614.70019 0 −1.18515 14.6274 0 −1.25919 14.49337 0 −1.3527 14.32179 0−1.46778 14.1109 0 −1.6054 13.85904 0 −1.76616 13.56515 0 −1.9501113.22862 0 −2.15749 12.84962 0 −2.3882 12.42884 0 −2.64222 11.96759 0−2.92325 11.46988 0 −3.23681 10.94161 0 −3.58506 10.38743 0 −3.969389.812155 0 −4.39031 9.220663 0 −4.84725 8.617659 0 −5.33833 8.007425 0−5.86052 7.393652 0 −6.40992 6.779433 0 −6.98201 6.167327 0 −7.571895.559478 0 −8.17475 4.957908 0 −8.79254 4.371587 0 −9.42637 3.809613 0−10.0802 3.286086 0 −10.7579 2.819148 0 −11.4603 2.429108 0 −12.18232.135349 0 −12.9115 1.953196 0 −13.6289 1.890063 0 −14.3122 1.941846 0−14.942 2.092473 0 −15.5061 2.317726 0 −16.0008 2.590757 0 −16.42892.886518 0 −16.7969 3.183881 0 −17.1139 3.466274 0 −17.3905 3.720994 0−17.6389 3.937206 0 −17.8711 4.103734 0 −18.0915 4.207451 0 −18.28584.240589 0 −18.4304 4.219173 0 −18.5228 4.175713 0 −18.7398 4.2196580.07975 −18.7782 4.180056 0.07975 −18.8256 4.115458 0.07975 −18.87744.003318 0.07975 −18.9082 3.833949 0.07975 −18.8949 3.609554 0.07975−18.8254 3.337302 0.07975 −18.6948 3.024228 0.07975 −18.501 2.6755490.07975 −18.242 2.296279 0.07975 −17.9155 1.892408 0.07975 −17.51841.471464 0.07975 −17.0475 1.043126 0.07975 −16.4995 0.62014 0.07975−15.8722 0.217715 0.07975 −15.1638 −0.14328 0.07975 −14.3761 −0.439010.07975 −13.5161 −0.64109 0.07975 −12.5987 −0.7211 0.07975 −11.647−0.6531 0.07975 −10.692 −0.42453 0.07975 −9.76438 −0.03868 0.07975−8.88771 0.48684 0.07975 −8.07573 1.126914 0.07975 −7.33308 1.8550220.07975 −6.65803 2.646649 0.07975 −6.04521 3.480644 0.07975 −5.488124.339589 0.07975 −4.98278 5.21065 0.07975 −4.52301 6.081571 0.07975−4.10232 6.941539 0.07975 −3.71661 7.782122 0.07975 −3.36259 8.596080.07975 −3.0371 9.376919 0.07975 −2.73683 10.11874 0.07975 −2.4610210.81727 0.07975 −2.20777 11.46835 0.07975 −1.97594 12.06872 0.07975−1.76543 12.61615 0.07975 −1.57577 13.10893 0.07975 −1.40702 13.546250.07975 −1.25889 13.92793 0.07975 −1.13132 14.25469 0.07975 −1.0239314.52797 0.07975 −0.9361 14.75006 0.07975 −0.8675 14.92423 0.07975−0.84702 15.06147 0.07975 −0.88701 15.1497 0.07975 −0.93133 15.192140.07975 −0.97281 15.21464 0.07975 −1.01195 15.22608 0.07975 −1.0649615.22911 0.07975 −1.14535 15.20647 0.07975 −1.23054 15.12239 0.07975−1.30627 14.97963 0.07975 −1.40189 14.79695 0.07975 −1.51897 14.572080.07975 −1.6581 14.30308 0.07975 −1.81963 13.98866 0.07975 −2.003813.62827 0.07975 −2.21022 13.2218 0.07975 −2.43864 12.76985 0.07975−2.68893 12.27376 0.07975 −2.96169 11.73578 0.07975 −3.25867 11.159380.07975 −3.58341 10.54949 0.07975 −3.93671 9.910228 0.07975 −4.318759.24588 0.07975 −4.72887 8.560732 0.07975 −5.16761 7.860206 0.07975−5.63541 7.150146 0.07975 −6.13251 6.43676 0.07975 −6.65964 5.7271420.07975 −7.21797 5.029404 0.07975 −7.80986 4.353581 0.07975 −8.435163.70886 0.07975 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6.01137 1 −11.0041 5.330791 1 −11.7539 4.69367 1−12.5314 4.115456 1 −13.3408 3.622347 1 −14.1778 3.246589 1 −15.02383.015009 1 −15.8475 2.939162 1 −16.6187 3.010356 1 −17.3191 3.204949 1−17.9416 3.490762 1 −18.4933 3.828794 1 −18.9898 4.177159 1 −19.44834.494721 1 −19.8837 4.750404 1 −20.2981 4.924827 1 −20.6793 5.012375 1−21.009 5.02372 1 −21.2741 4.982311 1 −21.4751 4.914073 1 −21.62034.839937 1 −21.7181 4.774886 1 −23.3299 5.532897 1.10225 −23.38 5.4794461.10225 −23.45 5.399833 1.10225 −23.5514 5.272023 1.10225 −23.67945.083594 1.10225 −23.8205 4.821176 1.10225 −23.9494 4.473049 1.10225−24.0254 4.032027 1.10225 −24 3.507811 1.10225 −23.8313 2.927027 1.10225−23.5116 2.320905 1.10225 −23.0659 1.700348 1.10225 −22.5177 1.0619251.10225 −21.8747 0.408815 1.10225 −21.1339 −0.2439 1.10225 −20.2891−0.86925 1.10225 −19.3368 −1.42817 1.10225 −18.2734 −1.87661 1.10225−17.1008 −2.16119 1.10225 −15.8475 −2.22301 1.10225 −14.5684 −2.018961.10225 −13.3258 −1.55648 1.10225 −12.1709 −0.85918 1.10225 −11.13630.031003 1.10225 −10.2259 1.059055 1.10225 −9.42411 2.174289 1.10225−8.70982 3.339092 1.10225 −8.07023 4.529886 1.10225 −7.49191 5.7271111.10225 −6.96055 6.91385 1.10225 −6.46891 8.078303 1.10225 −6.015419.212045 1.10225 −5.58819 10.30331 1.10225 −5.18128 11.34346 1.10225−4.7944 12.32669 1.10225 −4.42321 13.24613 1.10225 −4.07702 14.101041.10225 −3.75883 14.88892 1.10225 −3.46708 15.60622 1.10225 −3.2006116.2504 1.10225 −2.95989 16.82055 1.10225 −2.74531 17.31668 1.10225−2.5578 17.74014 1.10225 −2.39782 18.09326 1.10225 −2.26534 18.379391.10225 −2.16015 18.60311 1.10225 −2.09715 18.77609 1.10225 −2.1251218.90015 1.10225 −2.17753 18.96192 1.10225 −2.23053 18.99457 1.10225−2.27399 19.00846 1.10225 −2.33325 19.01279 1.10225 −2.42318 18.986661.10225 −2.51586 18.89097 1.10225 −2.6025 18.73217 1.10225 −2.7133118.5298 1.10225 −2.85022 18.28135 1.10225 −3.01448 17.98495 1.10225−3.20696 17.6394 1.10225 −3.42785 17.24407 1.10225 −3.67734 16.799131.10225 −3.95472 16.30504 1.10225 −4.26003 15.76341 1.10225 −4.593215.17647 1.10225 −4.95421 14.54712 1.10225 −5.34676 13.88114 1.10225−5.7759 13.18583 1.10225 −6.24727 12.4699 1.10225 −6.7658 11.743061.10225 −7.33445 11.01497 1.10225 −7.95328 10.29427 1.10225 −8.61929.587569 1.10225 −9.32684 8.898195 1.10225 −10.0682 8.227247 1.10225−10.8335 7.573987 1.10225 −11.6124 6.937926 1.10225 −12.4018 6.3236741.10225 −13.2038 5.740616 1.10225 −14.0254 5.209872 1.10225 −14.86874.76779 1.10225 −15.7157 4.457654 1.10225 −16.5294 4.30886 1.10225−17.2856 4.319483 1.10225 −18.0023 4.471478 1.10225 −18.6911 4.7474451.10225 −19.3193 5.087192 1.10225 −19.8893 5.422071 1.10225 −20.42655.70775 1.10225 −20.9428 5.921703 1.10225 −21.4314 6.052959 1.10225−21.8762 6.101763 1.10225 −22.2594 6.081163 1.10225 −22.5755 6.010471.10225 −22.8248 5.910596 1.10225 −23.0126 5.802347 1.10225 −23.14635.70321 1.10225 −23.2363 5.624802 1.10225 −24.9622 6.471759 1.2045−25.0177 6.413143 1.2045 −25.0959 6.326439 1.2045 −25.2112 6.1887711.2045 −25.3612 5.988286 1.2045 −25.5368 5.712608 1.2045 −25.72185.347277 1.2045 −25.8851 4.882125 1.2045 −25.9823 4.311508 1.2045−25.955 3.647588 1.2045 −25.753 2.921472 1.2045 −25.3731 2.171679 1.2045−24.8405 1.413154 1.2045 −24.1749 0.654108 1.2045 −23.3962 −0.104811.2045 −22.5176 −0.86302 1.2045 −21.5391 −1.60564 1.2045 −20.4507−2.28915 1.2045 −19.2342 −2.82941 1.2045 −17.8915 −3.14961 1.2045−16.4685 −3.19316 1.2045 −15.0342 −2.9314 1.2045 −13.6589 −2.375511.2045 −12.4055 −1.55106 1.2045 −11.312 −0.51104 1.2045 −10.38630.681943 1.2045 −9.59362 1.958472 1.2045 −8.90393 3.275616 1.2045−8.28879 4.602402 1.2045 −7.73091 5.919336 1.2045 −7.21153 7.2090091.2045 −6.72267 8.460006 1.2045 −6.26594 9.665412 1.2045 −5.8267210.81276 1.2045 −5.39956 11.89362 1.2045 −4.98425 12.90208 1.2045−4.58226 13.83357 1.2045 −4.21245 14.69193 1.2045 −3.87642 15.47461.2045 −3.56942 16.17726 1.2045 −3.29238 16.79906 1.2045 −3.0448217.33964 1.2045 −2.82761 17.80042 1.2045 −2.64157 18.18411 1.2045−2.48697 18.49457 1.2045 −2.36363 18.73692 1.2045 −2.27975 18.921581.2045 −2.29982 19.06005 1.2045 −2.35489 19.12992 1.2045 −2.4124819.16688 1.2045 −2.45711 19.18155 1.2045 −2.51804 19.1867 1.2045−2.61131 19.16111 1.2045 −2.70563 19.06212 1.2045 −2.79758 18.900141.2045 −2.91572 18.69404 1.2045 −3.06266 18.44161 1.2045 −3.2400518.14114 1.2045 −3.44911 17.79164 1.2045 −3.69032 17.3926 1.2045−3.96425 16.94446 1.2045 −4.2698 16.44745 1.2045 −4.60824 15.904041.2045 −4.97929 15.31648 1.2045 −5.37947 14.68565 1.2045 −5.8208814.02312 1.2045 −6.31967 13.34521 1.2045 −6.87918 12.66237 1.2045−7.50194 11.98619 1.2045 −8.18221 11.32108 1.2045 −8.912 10.66872 1.2045−9.68289 10.02705 1.2045 −10.484 9.393163 1.2045 −11.3002 8.7665381.2045 −12.1209 8.148168 1.2045 −12.9464 7.542622 1.2045 −13.78726.963119 1.2045 −14.6611 6.433849 1.2045 −15.5763 5.995771 1.2045−16.4793 5.707533 1.2045 −17.2262 5.592283 1.2045 −17.8647 5.5911651.2045 −18.6516 5.714962 1.2045 −19.4331 5.963084 1.2045 −20.14596.272658 1.2045 −20.7944 6.58711 1.2045 −21.4075 6.87325 1.2045 −21.99977.10298 1.2045 −22.5631 7.251128 1.2045 −23.08 7.307181 1.2045 −23.53537.278052 1.2045 −23.9198 7.17959 1.2045 −24.2276 7.042706 1.2045−24.4659 6.895775 1.2045 −24.6454 6.761611 1.2045 −24.7762 6.6509321.2045 −24.8666 6.567428 1.2045 −24.9236 6.511329 1.2045

In the above Table 1, the plane Zadim=0 corresponds to the referenceplane P0 situated at the base of the profile. This plane P0 is theintersection of the stacking axis AE of the set of vanes with theaxisymmetric surface of the hub, i.e. it passes via the intersectionbetween the axis AE and the surface 16A where it is assembled with theinner shroud 16. The plane Zadim=1 corresponds to the reference plane P1situated at the top of the profile. This plane P1 is the intersectionbetween the axis AE and the axisymmetric surface of the casing, i.e. itpasses via the intersection of the axis AE with the surface 12A where itis assembled with the outer ring 12.

By convention, the stacking axis AE of the set of vanes, for the vane ofa nozzle, is the axis that extends in the radial direction Z and passesthrough the middle of the inter-vane throat. For a given vane, theinter-vane throat is the location where the distance between thetrailing edge of the vane in question and the suction side of thepreceding vane in the direction of rotation of the turbine is at aminimum.

This is the axis on which the various X,Y sections of the set of vanesare “stacked” when designing the set of vanes.

As mentioned at the beginning of the present description, theaerodynamic profile of the invention is substantially identical to thenominal profile defined in the above table, i.e. it departs from saidnominal profile by very little at most, being defined in particularwithin an envelope of ±1 mm in a direction normal to the surface of thenominal profile, and/or having X,Y coordinates lying within a range of±5% relative to the coordinates X,Y of the nominal profile.

The coordinate Zadim is non-dimensional, i.e. for a point P, situated ata distance D from the plane P0 (where D is measured along the axis Z),the value of Zadim is D/H, where H represents the total height of theprofile as measured between the planes P0 and P1. Naturally, in theTable 1 above, by multiplying the coordinate Zadim by the height H, itis possible to obtain the complete coordinates of the vane.

By way of example, the total height H is preferably about 115 mm±10%. Byway of example, the plane P0 is situated at a distance of about 415mm±10% from the axis A.

In the above table, the profile is characterized by seventeen sectionplanes at constant Zadim coordinates, for which the coordinates X and Yare specified. These seventeen section planes include thirteen sectionplanes located between Zadim=0 and Zadim=1, and thus arranged in thefluid stream, these section planes being distributed from P0 to P1. Theseventeen section planes also include four section planes which aresubstantially outside the fluid stream (two section planes with Zadim<0,and two section planes with Zadim>1), these four section planes beingprovided for ensuring geometric continuity of the stacking, close to thehead and the foot, respectively. In each section plane at constantcoordinate Zadim, the section of the profile is given by a continuousand smooth curve, interconnecting all of the points (X,Y). In eachsection plane, the profile is interpolated so as to generate a uniformprofile. Between the section planes, the profile is to be interpolatedso as to generate a complete vane, as homogeneous as possible.

It is advantageous for the nozzle that includes the vane of theinvention to have 140 to 160 vanes that present aerodynamic profiles asdefined above.

We claim:
 1. An aerodynamic profile for a turbine vane, the profilebeing, when cold and in a non-coated state, substantially identical to anominal profile determined by the Cartesian coordinates X,Y,Zadim givenin Table 1, in which the coordinate Zadim is the quotient D/H, where Dis the distance of the point under consideration from a reference X,Yplane situated at the base of the nominal profile, and H is the heightof said profile measured from said reference plane out to the end of thevane, the measurements D and H being taken radially relative to the axisof the turbine, while the coordinate X is measured in the axialdirection of the turbine.
 2. The aerodynamic profile as claimed in claim1, wherein said profile is defined within an envelope of ±1 mm in adirection normal to the surface of the nominal profile.
 3. Theaerodynamic profile as claimed in claim 1, wherein the coordinates X,Yof said profile lie within a range of ±5% relative to the coordinatesX,Y of the nominal profile.
 4. The aerodynamic profile as claimed inclaim 1, wherein the vane is a nozzle vane forming a part of a stator ofa turbine.
 5. The aerodynamic profile as claimed in claim 4, wherein thevane is a nozzle vane of the fourth stage of the turbine.
 6. Theaerodynamic profile as claimed in claim 4, wherein the vane is a vane ofthe fourth stage nozzle of a turbine having seven stages.
 7. A turbinevane, presenting an aerodynamic profile as claimed in claim
 1. 8. Aturbine, including turbine vanes presenting aerodynamic profiles asclaimed in claim
 1. 9. A turbine as claimed in claim 8, including anozzle that is stationary in rotation, having 140 to 160 vanes thatpresent aerodynamic profiles comprising: when cold and in a non-coatedstate, substantially identical to a nominal profile determined by theCartesian coordinates X,Y,Zadim given in Table 1, in which thecoordinate Zadim is the quotient D/H, where D is the distance of thepoint under consideration from a reference X,Y plane situated at thebase of the nominal profile, and H is the height of said profilemeasured from said reference plane out to the end of the vane, themeasurements D and H being taken radially relative to the axis of theturbine, while the coordinate X is measured in the axial direction ofthe turbine.
 10. A turbine nozzle forming a portion of a turbine stator,wherein all the vanes of the nozzle present an aerodynamic profile asclaimed in claim
 1. 11. A turbine nozzle as claimed in claim 10,including 140 to 160 vanes that present aerodynamic profiles comprising:when cold and in a non-coated state, substantially identical to anominal profile determined by the Cartesian coordinates X,Y,Zadim givenin Table 1, in which the coordinate Zadim is the quotient D/H, where Dis the distance of the point under consideration from a reference X,Yplane situated at the base of the nominal profile, and H is the heightof said profile measured from said reference plane out to the end of thevane, the measurements D and H being taken radially relative to the axisof the turbine, while the coordinate X is measured in the axialdirection of the turbine.